What is the Least Common Multiple of 36780 and 36800?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 36780 and 36800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36780 and 36800, than apply into the LCM equation.

GCF(36780,36800) = 20
LCM(36780,36800) = ( 36780 × 36800) / 20
LCM(36780,36800) = 1353504000 / 20
LCM(36780,36800) = 67675200

Least Common Multiple (LCM) of 36780 and 36800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36780 and 36800. First we will calculate the prime factors of 36780 and 36800.

Prime Factorization of 36780

Prime Factorization of 36800

Now multiplying the highest exponent prime factors to calculate the LCM of 36780 and 36800.

LCM(36780,36800) = 2⁶ × 3¹ × 5² × 613¹ × 23¹
LCM(36780,36800) = 67675200